层合板分叉方程的Lyapunov-Schmidt约化分析

The Lyapunov-Schmidt Reduction Analyse of Laminated Plates Bifurcation Equations

采用广义傅立叶级数法建立了具有弹性约束的复合材料矩形层板在面内载荷作用下的非线性稳定性控制方程组 ,并简化为矩阵形式。利用分叉理论和泛函知识 ,对有限维的该分叉方程进行了Lyapunov Schmidt约化 ,获得了三种典型的分叉图形式 ,同时指出当非齐次项等于零时必然发生分叉。数值计算结果指明了三种分叉图分别所对应的典型的力学模型 ,主要因素在于边界条件、铺层方式及初始缺陷三方面。

The nonlinear governing equations of rectangular composite laminated plates with edges elastically supported against rotation are established by generalized Fou rier series method. The governing equations are simplified in matrix form. The f inite dimension bifurcation equations are Lyapunov-Schmidt reduced by the bifur c ation theoretics and the functional knowledge. Three typical bifurcation figure forms are achieved, and it is pointed out that the bifurcation should take place consequentitally as the non-homogeneous term equals to zero. The numerically c o mputational results show the mechanical models corresponding to these three kind s of bifurcation figures containing various boundary conditions, lay up sequence and initial imperfections.